A nationwide shortage of warehouse space that drove a yearslong surge in rents is showing signs of easing, the chief executive of the biggest owner of U.S. industrial real estate said Tuesday.

Warehouse demand has outpaced new supply since the end of the recession, as economic growth picked up. Retailers also stepped up leasing as online orders rose. The cost of renting space has soared, particularly in urban areas such as Los Angeles and Seattle, where less than 5% of total warehouse capacity is available for leasing, according to
CBRE Group Inc.

At the end of last year, supply began to catch up with demand, said
Hamid Moghadam,
chairman and chief executive of Prologis Inc., in an interview.

“New construction has been relatively disciplined, so the market is much stronger,” Mr. Moghadam said in an interview. “Now we are getting into the more mature part of the cycle. It’s more of a balanced market, with modest rental growth.”

Occupancy rates at Prologis facilities hit 97.1% in the fourth quarter—an all-time high. Rents in the U.S. jumped by more than 23%, with global rates increasing by 16%, the company said.

Prologis shares closed down 1.9% at $51.83 Tuesday afternoon in New York.

The warehouse market appears to be stabilizing even as online sales growth shows no signs of slowing.

Online sales increased nearly 11% this holiday season compared with the same time last year, according to estimates by
First Data Corp.
, which tracked credit, debit and other card transactions at one million U.S. merchants. In 2016, spending at online retailers was up 11%, while spending at department stores fell nearly 6%, according to the Commerce Department.

CBRE said in a report last week it expects industrial real-estate completions to consistently top 50 million square feet per quarter this year, a key threshold that usually signals stable availability rates.

The broker said last week U.S. industrial space available to rent fell by five basis points to 8.2% in the fourth quarter, the smallest decline since 2010. That still put availability at a 15-year low.

Rent growth is expected to flatten out as supply and demand continue to equalize,
Jeffrey Havsy,
CBRE’s chief economist for the Americas, said in a statement.

This year “vacancy rates are going to stay basically stable,” Mr. Moghadam said.